Hello Document ... I'm far from a Simpson Bay expert but if memory serves me right there's a small public parking lot behind Captain's Rib Shack right off Welfare Road. Kim Sha beach is literally right there. Not huge, so I would suggest getting there early but this is one area that I am aware of. Hope this helps.
For Little Bay: Yes, just tell the guard at the gate you are going to the beach and they will let you through, then park in the Divi lot. Very convenient.